{
"cells": [
{
"cell_type": "markdown",
"id": "84e56e0e",
"metadata": {},
"source": [
"# Pulsed-DNP: NOVEL"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "86dbd821",
"metadata": {},
"source": [
"Nuclear Overhauser effect Via Electron spin-Locking (NOVEL)$^1$ is a DNP transfer mechanism which occurs by matching a spin-lock applied to electrons to the nuclear Larmor frequency. The sequence needs to be repeated many times to build up bulk nuclear polarization. Here we set up the transfer, and investigate some simple improvements to make the transfer more efficient.\n",
"\n",
"[1] A. Henstra, P. Dirksen, J. Schmidt, W. Th. Wenckebach. [*J. Magn. Reson.*](https://doi.org/10.1016/0022-2364(88)90190-4), **1988**, 77, 389-393."
]
},
{
"cell_type": "markdown",
"id": "b2ac3a97",
"metadata": {},
"source": [
"## Setup"
]
}
,
{
"cell_type": "code",
"execution_count": 0,
"metadata": {"tags": [
"remove-cell"
]},
"outputs": [],
"source": [
"# SETUP SLEEPY\n",
"import sys\n",
"if 'google.colab' in sys.modules:\n",
" !pip install sleepy-nmr"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "d864fb80",
"metadata": {},
"outputs": [],
"source": [
"import SLEEPY as sl\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"id": "f6998a34",
"metadata": {},
"source": [
"## Build the system"
]
},
{
"cell_type": "markdown",
"id": "c7d870bd",
"metadata": {},
"source": [
"We build an electron-nuclear system, noting that the nucleus needs to be in the lab frame, since the pseudosecular hyperfine coupling drives NOVEL transfer. We start monitoring magnetization during a single NOVEL sequence (a $pi/2$-pulse followed by a spin-lock)."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "dcc7e90a",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ex=sl.ExpSys(v0H=212,Nucs=['1H','e'],vr=0,LF=[True,False],T_K=80,pwdavg=2)\n",
"delta=4e5\n",
"ex.set_inter('hyperfine',i0=0,i1=1,Axx=-delta/2,Ayy=-delta/2,Azz=delta)\n",
"\n",
"L=ex.Liouvillian()\n",
"\n",
"# Note that because the nuclear quantization axis is tilted away from z, \n",
"# it is important to set OS=True\n",
"L.add_relax(Type='T2',i=0,T2=5e-3,OS=True)\n",
"L.add_relax(Type='T2',i=1,T2=.890e-6,OS=True)\n",
"L.add_relax(Type='T1',i=0,T1=13.7,OS=True,Thermal=True)\n",
"L.add_relax(Type='T1',i=1,T1=1.4e-3,OS=True,Thermal=True)\n",
"\n",
"v1=212e6\n",
"pi2=1/v1/4\n",
"SL=2e-5\n",
"\n",
"seq=L.Sequence().add_channel('e',t=[0,pi2,pi2+SL],v1=[v1,v1],phase=[0,np.pi/2])\n",
"\n",
"rho=sl.Rho('Thermal',['1Hz','ez','ey'])\n",
"rho.DetProp(seq,n=100,n_per_seq=100)\n",
"_=rho.plot(axis='us')"
]
},
{
"cell_type": "markdown",
"id": "726c7f10",
"metadata": {},
"source": [
"We monitor electron *z*- and *y*-magnetization, where an initial $\\pi$/2-pulse on the electron converts all electron *z*-magnetization to *y*-magnetization. That magnetization is then transferred $z$-magnetization on the nucleus. However, it also decays primarily due to the electron $T_2$ relaxation. Then, we see that the length of the transfer could be optimized to minimize this loss, by setting the transfer time near to where the maximum nuclear polarization occurs. We add a recycle delay (`RD`) to see what happens to the magnetization after the transfer."
]
},
{
"cell_type": "markdown",
"id": "d47f8e53",
"metadata": {},
"source": [
"### Stop transfer after maximum reached"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "53493508",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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cT8PdG4F2N8Nw923AeQXTS4AlRdZ7FHg0yhrbStWkyDQHSBe7sJbvXM6UIVMYccyICCoTEYmHzkQPKT+I3hwg4XM3k8vwwq4XdPiuiPQ6CpCQkjVJMuTyh4ElwgfIujfXsT+9X91XItLrKEBCSgXdVhnoUgtkVeMqAE4ZeUoEVYmIxEcBElJzgKTNujQGsqZxDYP7DWbCoAlRlSYiEgsFSEipREGAdOEorNWNq5leN123rxWRXkcBElLS8t1WaSP0eSDpXJp1b65j2vBpEVYmIhIPBUhILS0QwndhbXxrI+lcmunDp3e+sojIUUYBElLLILpZ6EH01Y2rAZhWpxaIiPQ+CpCQjgyi06UAGZgayKRjJ0VYmYhIPBQgIR0JkATUhNtta/as4aS6k6gx7WYR6X30zRZSMmh1pEOeRJjNZVm7Z626r0Sk11KAhNQyBhLyEN5NTZs4lD2kAXQR6bUUICG1HIXVhe4r0AC6iPReCpCQWsZAujCAXpuoZfKQyVGWJSISmy4FiJn9hZn1yWuSt4yBhDyJcHXjak6sO5FEF28+JSJytAgdIGY2g/yNnz4TWTU9WMsYSIgWSM5zvLrnVXVfiUiv1pUWyFXAl4ErIqqlRzvShdX5LtuydwsHMgc0gC4ivVqoADGz/uTvFHgXsMHMzoy0qh7oSIB03iW19s21AJxUd1KkNYmIxClsC+RjwBPu/g6wiHxrpE/pyhjIxqaNGEb9kPqIqxIRiU/YALkKWBg8XwK838wGRVNSz9R8GG8mxGXZNzVtYtygcRyTPCbqskREYtNpgJjZUGCbu78A4O5Z4DZgdrSl9Sxd6cJ6rek1tT5EpNfr9JAid38L+HSbed+LqqCe6si1sDrO3Jzn2NS0iVljZlWjLBGR2IQ6K87MaoFrgTMBB54G7nD3QxHW1qO0jIF0EiA79u/gUPaQTiAUkV4v3GnV8ADwNvAvwfTlwL8Cl0RRVE/UHCCZmo7HQDY2bQRgypApkdckIhKnsAFyoru/p2D6l2b2UhQF9VQ1VkPSg3uid2BT0yYAtUBEpNcLexTWC2Z2RvOEmZ0OPBNNST1Xis5PJNzYtJGh/YdSV1tXnaJERGIStgVyOnCFmW0JpicBa8zsZcDdfUYk1fUwSYI7EnZgU9MmtT5EpE8IGyBzI63iKJFyyNB5F9YHJ36wShWJiMQnbIBMAU4mfwTWanf/ZXQl9Vz5FkjpAHnr0FvsObRHLRAR6RM6DBAzGw/8GDgErAAMuNTMvgVc5O5boy+x50h5x11Ym/ZqAF1E+o7OWiC3kT/f4/uFM83sCuD/AfMiqqtHSrmT7mC5jsASkb6ks6OwprcNDwB3fwDoc5eaTdJxgGx8ayP9avoxbuC4qtUkIhKXzgKk6IWfzKym1LIwzKzOzJ40s/XB47AS6801s7VmtsHMFhTM/46ZvWpmK83s0eB6XZFLuZPppAurfki97kIoIn1CZwHyH2Z2j5kNbJ4RPL+T/FV5y7UAWOruU4GlwXQrZpYAbgfOBaYDl5tZ8x2angTeHRw+vA74m27UElqYLix1X4lIX9FZgHwZaAI2m9kKM1sOvAbsBW7oxvvOA+4Pnt8PXFhkndnABnff6O6HgR8G2+HuP3P3TLDes8CEbtQSWiqXI40XXfZO9h227tuqS5iISJ/R4SC6u6eBG8zs/wAnkD8Ka4O7H+jm+4529+3Be2w3s1FF1hkPvF4w3UD+hMa2PgssLvVGZnYNcA3ApEmTyi4YIOk53ikRIJv3bibnObVARKTP6PQ8EDMbAEx195cK5k0Csh0dxmtmPwfGFFl0Y8jaio02tPr2NrMbgQzwUKkXcfe7gbsBZs2aVfzbPwx3Uu7sLxEgOgJLRPqaMCcSpoEfm9kMd98fzLsX+CpQMkDc/exSy8xsp5mNDVofY4FdRVZrACYWTE8AthW8xnzgfOAsdy8/GMLKZfJjICXe6vW3842lSYO718oRETladHoxxaAb61HgMmhpfYx09+XdeN/HgPnB8/nAT4usswyYamaTzawf8IlgO8xsLvAV4IIKdKeF0xwg5Iou3rpvK8P6D2NAakBVyhERiVvYq/HeC1wZPL8CWNTN970FOMfM1gPnBNOY2TgzWwIQDJJfBzwBrAEedvdVwfa3AYOBJ83sRTO7s5v1dC6bzl/KpEQX1ta3tzJ+0PjIyxAR6SlCXQvL3V81M8zsXeRvJnVmd97U3RuBs4rM3wacVzC9hCKHC7v7Cd15/7IELZCMl26BTBs+rcpFiYjEJ2wLBGAh+ZbISnd/M6J6eq6WMZD2AZLNZdm2fxvjBukMdBHpO7oSIA8D7yEfJH1PNp2/mGKRMZDdB3eTyWWYMKgqp6OIiPQIYS/nTjBYPSTCWnq2XCZ/LawiLZCt+/IHo2kMRET6kq60QPq2ljGQbLtFChAR6YsUIGHlMvkuLM/S9rSTrW9vxTCNgYhIn6IACSubJoXjQLZNK6RhXwMjB4ykX6JfPLWJiMRAARJWLk0qaHmkc62vybt131YNoItIn6MACSuXJRn0XGVymVaLtu7TSYQi0vcoQMLKFm+BpLNpdu7fyfjBChAR6VsUIGHlMqSCy5iks0cCZPv+7Tiu29iKSJ+jAAkrlz+REFq3QBr2NQAwYbDGQESkb1GAhJXLkgy6sArHQHQOiIj0VQqQsEqMgWx9eytJSzJ6wOi4KhMRiYUCJKxcmlTwtDBAtu3bxpiBY0jUJOKpS0QkJgqQsIJLmUCbFsi+rToCS0T6JAVIWNlMyxhI4VFYDfsadBKhiPRJCpCwgmthAWQ8P4h+IH2APYf2aABdRPokBUhYuXS780C27dsGoIsoikifpAAJq8hRWDqEV0T6MgVIWAXXwmobIDqJUET6IgVIWAVX420+kXDngZ0ka5LU1dbFWZmISCwUIGEVXgsraIHsOrCLUceMosa0G0Wk79E3X1jZTLtrYe06sItRA0bFWJSISHwUIGHl2p8HogARkb5MARJWLk0q2F2ZXAZ3Z+eBnQoQEemzFCBhZdOkEkkg34W1L72Pg5mDuoiiiPRZCpCwcllSdiRAdh3YBaAWiIj0WQqQsHJpEjVJaqyGdC7NzgM7AQWIiPRdCpCwchlIpEhakkwu09ICUReWiPRVybgLOGpk01CTJJVIterCGjlgZMyFiUg50uk0DQ0NHDp0KO5Seoza2lomTJhAKpXqfGUUIOHlMlCTIlWTIp3NB8iQ/kOoTdbGXZmIlKGhoYHBgwdTX1+PmcVdTuzcncbGRhoaGpg8eXKobdSFFVYuAzWJfIAEYyAa/xA5eh06dIjhw4crPAJmxvDhw7vUIoslQMyszsyeNLP1weOwEuvNNbO1ZrbBzBYUzP97M1tpZi+a2c/MLPrrqWfT+TGQmiNjIAoQkaObwqO1ru6PuFogC4Cl7j4VWBpMt2JmCeB24FxgOnC5mU0PFn/H3We4+6nAfwJfi7ziwi6sYAxEA+gi0pfFFSDzgPuD5/cDFxZZZzawwd03uvth4IfBdrj73oL1BkJwlcMoFXRhHcwcpPFgo1ogItKnxRUgo919O0DwWOybeDzwesF0QzAPADP7v2b2OvBndNACMbNrzGy5mS3fvXt3+RUHh/GmEil27N+B4woQEYnUxo0bueqqq/j4xz8edylFRRYgZvZzM3ulyM+8sC9RZF5LS8Pdb3T3icBDwHWlXsTd73b3We4+a+TIbhxyGxzGm7Rky42k1IUlIlGaMmUKCxcubDf/rrvu4tprr2017+STT+bVV1+tVmlAhIfxuvvZpZaZ2U4zG+vu281sLLCryGoNwMSC6QnAtiLr/RvwX8DfdqfeTjWPgSRS7D2c70FTC0REonD48GHS6TQDBw4sunzlypWcdtppLdOHDh1iy5YtTJ06td26b775JsOGFT1Oqdvi6sJ6DJgfPJ8P/LTIOsuAqWY22cz6AZ8ItsPMCvfSBUD0sVswBtJMASIilbRmzRr+6q/+ihNPPJF169aVXO/ll19m5syZrabf9a53kUgk2q07a9YsPvnJT/KLX/wC98oOF8cVILcA55jZeuCcYBozG2dmSwDcPUO+a+oJYA3wsLuvat4+6A5bCcwBro+84uAw3uYASdWkGNY/mlQXkb5j//79LFq0iDPPPJOrr76aadOmtbQwGhsb+cIXvsALL7zAzTff3LLNqlWruPjii6mvr6e+vp5zzz2XU045pejrr1u3jk9+8pPcdtttTJ8+nW9+85ts21asM6frYjkT3d0bgbOKzN8GnFcwvQRYUmS9j0VaYDFBF1ayJr/LRg0YpWPIRXqJv/uPVazetrfzFbtg+rhj+duPntzpemPHjmXGjBnce++9nHTSSa2WDR8+nDvvvLPVvNdff52RI0e2Gu+47rrrmDJlStHXTyQSnH/++Zx//vns3r2bv/mbv2HSpEn89re/Zfbs2WX8y47QmehhtenCUveViFTCI488wvjx47nooov4+te/zubNmztcf+XKlZx8cutgWr16dckWCEBTUxN33303F1xwAevWrWPhwoXMmDGj27XrWlhhtenCUoCI9B5hWgpRmTNnDnPmzKGxsZEHH3yQefPmMWLECO69917q6+vbrf/yyy8zffr0VvNWrVrFjBkz2Lx5M/fccw+bNm3CzHjwwQf51Kc+xe9+9zsuueQSHnjggaID7eVSCySsXKblarygABGRyho+fDjXX389L774It/85jeLDohD+wDZs2cP7s7o0aM57rjjuOqqq0gkEtx1110AXHrppaxdu5ZbbrmlouEBaoGEV3ApE9A5ICISnY7GJh566KFW03V1dezalT8T4rXXXuOmm27ijjvuaDkE+IILLoisTrVAwsplIJFsNYguItKTnHfeedTV1XHzzTezZ8+eyN9PLZCwmm8opTEQEemhVq9eXdX3UwskrDZdWAoQEenrFCBhBYPo/RL9AAWIiIi6sMLKpiGR5OKpF3PC0BPon+gfd0UiIrFSgIQVtEDGDRrHuEHR3wBRRKSnUxdWGO7gWSi4kKKISF+nAAkjl8k/JtRgExFppgAJI5vOP9YoQEREmilAwsg1B4i6sEREmilAwshl849qgYiItFCAhNHchaUxEBGpgsOHD7N///4ubfPmm29GVE1pCpAwmgfR1YUlIhEqdkvbBx98kNmzZ3Pqqafy+c9/nmw2W3TbKG9dW4r+pA4jp0F0kV7t8QWw4+XKvuaYU+DcWzpdbf/+/Tz88MMsXLgQd+fKK69k5cqVDB48mDVr1rB48WKeeeYZUqkU1157LQ899BBXXHFFu9dZt24djz/+OLfddhtf+tKX+PSnP81nPvMZxo2L7rw1fSOG0TwGklALREQqq6Nb2i5dupQVK1bwR3/0RwAcPHiQUaOKX0YpylvXlqIACaPlMN7iN3gRkaNciJZCVB555BEWLlzIRRddxOWXX878+fM57rjjAHB35s+fz80339xqm2J3HoT8rWsXL17MokWLSKVSFbt1bSkaAwlDh/GKSETmzJnD4sWLefrppxkyZAjz5s3j7LPP5rXXXuOss87ikUceablh1J49e9i8eXPROw9+6lOfYubMmWzcuJEHHniAX//618yfP5/a2trIalcLJIyWQXTtLhGJRvMtba+//nqee+45EokE06dP5xvf+AZz5swhl8uRSqW4/fbbcfd2dx689NJL+f73v08yWb3vKX0jhpFtvpSJWiAiEr3CMYvLLruMyy67rNXy6dOn8+EPf5ibb76Zv/zLv6Suri7SW9eWogAJQy0QEelBqn3nwVI0BhKGDuMVEWlHARJGy5no6sISEWmmAAlD18ISEWlHARKGurBERNpRgISR01FYIiJtKUDC0A2lRETaUYCEoTEQEZF2FCBhaAxERKSdWALEzOrM7EkzWx88Diux3lwzW2tmG8xsQZHlN5iZm9mISAvWYbwiIu3E1QJZACx196nA0mC6FTNLALcD5wLTgcvNbHrB8onAOcCWyKvVDaVEpIrKuSMhVP+uhHEFyDzg/uD5/cCFRdaZDWxw943ufhj4YbBds+8BXwaiv/VWS4Docu4iEp3u3JEQqn9Xwrg69Ue7+3YAd99uZsXukDIeeL1gugE4HcDMLgC2uvtLZtbhG5nZNcA1AJMmTSqvWh3GK9Krfeu5b/Hqnlcr+pon1Z3EV2Z/pdP1KnVHQqj+XQkjCxAz+zkwpsiiG8O+RJF5bmYDgteYE+ZF3P1u4G6AWbNmlRfJOoxXRCJSqTsSQvXvShjZN6K7n11qmZntNLOxQetjLLCryGoNwMSC6QnANuB4YDLQ3PqYADxvZrPdfUfF/gGFNAYi0quFaSlEpZw7Ei5atIgxY8Ywd+5crrrqKm6//XaOOeYYoLp3JYxrDOQxYH7wfD7w0yLrLAOmmtlkM+sHfAJ4zN1fdvdR7l7v7vXkg2ZmZOEBGgMRkciUc0fC97///Tz99NMsXLiQyy67rCU8qn1Xwrj6ZG4BHjazq8gfRXUJgJmNA+519/PcPWNm1wFPAAngPndfFUu12XS++6qT8RYRkXJ15Y6EZ5xxBi+88AJNTU1cffXVLa9R7bsSxhIg7t4InFVk/jbgvILpJcCSTl6rvtL1tZPLqPtKRKqmszsSAiSTSb72ta+1mlftuxLqTPQwchkNoItIj9DU1MR1113H/PnzOxxQrwZ9K4aRTUNCu0pE4jdkyBBuu+22uMsAFCDhjDkFMgfjrkJEpEdRgITx3vn5HxERaaExEBERKYsCRET6rGpcL+po0tX9oQARkT6ptraWxsZGhUjA3WlsbOzSSYcaAxGRPmnChAk0NDSwe/fuuEvpMWpra5kwYULo9RUgItInpVIpJk+eHHcZRzV1YYmISFkUICIiUhYFiIiIlMX60hEIZrYb2Fzm5iOANypYTiX11NpUV9f11Np6al3Qc2vrqXVB12s7zt1Htp3ZpwKkO8xsubvPiruOYnpqbaqr63pqbT21Lui5tfXUuqBytakLS0REyqIAERGRsihAwrs77gI60FNrU11d11Nr66l1Qc+trafWBRWqTWMgIiJSFrVARESkLAoQEREpiwKkDTOba2ZrzWyDmS0ostzM7J+D5SvNbGYVappoZr80szVmtsrMri+yzgfMrMnMXgx+vhZ1XQXv/ZqZvRy87/Iiy+PYZycW7IsXzWyvmf1Fm3Wqts/M7D4z22VmrxTMqzOzJ81sffA4rMS2HX4mI6jrO2b2avC7etTMhpbYtsPfe0S13WRmWwt+Z+eV2Lba+2xxQU2vmdmLJbaNbJ+V+p6I9HPm7voJfoAE8AdgCtAPeAmY3mad84DHAQPOAH5fhbrGAjOD54OBdUXq+gDwnzHtt9eAER0sr/o+K/J73UH+ZKhY9hnwfmAm8ErBvG8DC4LnC4Bvlai9w89kBHXNAZLB828VqyvM7z2i2m4Cbgjx+67qPmuz/B+Ar1V7n5X6nojyc6YWSGuzgQ3uvtHdDwM/BOa1WWce8IDnPQsMNbOxURbl7tvd/fng+dvAGmB8lO9ZYVXfZ22cBfzB3cu9CkG3ufuvgT1tZs8D7g+e3w9cWGTTMJ/Jitbl7j9z90ww+SwQ/vreFVRin4VR9X3WzMwMuBT4QaXeL6wOvici+5wpQFobD7xeMN1A+y/qMOtExszqgdOA3xdZ/Mdm9pKZPW5mJ1erJsCBn5nZCjO7psjyWPcZ8AlK/4eOa58BjHb37ZD/zw+MKrJO3Pvus+Rbj8V09nuPynVB99p9Jbpj4txn/wPY6e7rSyyvyj5r8z0R2edMAdKaFZnX9jjnMOtEwswGAT8C/sLd97ZZ/Dz5Lpr3AP8C/KQaNQXe5+4zgXOBL5nZ+9ssj3Of9QMuAP69yOI491lYce67G4EM8FCJVTr7vUfhDuB44FRgO/nuorZi22fA5XTc+oh8n3XyPVFysyLzOt1nCpDWGoCJBdMTgG1lrFNxZpYi/6F4yN1/3Ha5u+91933B8yVAysxGRF1X8H7bgsddwKPkm8OFYtlngXOB5919Z9sFce6zwM7mrrzgcVeRdeL6vM0Hzgf+zINO8rZC/N4rzt13unvW3XPAPSXeM659lgQuBhaXWifqfVbieyKyz5kCpLVlwFQzmxz85foJ4LE26zwGXBEcWXQG0NTcPIxK0K+6EFjj7reWWGdMsB5mNpv877YxyrqC9xpoZoObn5MfgH2lzWpV32cFSv5FGNc+K/AYMD94Ph/4aZF1wnwmK8rM5gJfAS5w9wMl1gnze4+itsKxs4tKvGfV91ngbOBVd28otjDqfdbB90R0n7MojgY4mn/IHzG0jvwRCTcG874AfCF4bsDtwfKXgVlVqOlM8s3JlcCLwc95beq6DlhF/uiJZ4E/qdL+mhK850vB+/eIfRa87wDygTCkYF4s+4x8iG0H0uT/2rsKGA4sBdYHj3XBuuOAJR19JiOuawP5/vDmz9qdbesq9XuvQm3/GnyGVpL/ghvbE/ZZMP/7zZ+tgnWrts86+J6I7HOmS5mIiEhZ1IUlIiJlUYCIiEhZFCAiIlIWBYiIiJRFASIiImVRgIiISFkUICIiUhYFiEgEzGyomV3byTp3mdn7qlWTSKUpQESiMRToMECA08mfAS9yVFKAiETjFuD44M5z32m70MymAevcPdtm/lNmdmLwfHjzXe+C6yj9V3Dp+VfM7LJq/CNEOpKMuwCRXmoB8G53P7XE8nOB/y4y/wTy1ywCmEH+uk8Ac4Ft7v4RADMbUrlSRcqjFohIPD5MmwAxs+OArZ6/VDnkA2Rl8Pxl4Gwz+5aZ/Q93b6peqSLFKUBEqszMBgBDPbg3RIFTORIYAO9tnnb3dcH0y8DNZva1KpQq0iEFiEg03gYGl1j2QeCXRea/B6gFMLOp5O9J/XIwPQ444O4PAt8FZla6YJGuUoCIRMDdG4FnggHvtoPopcY/TgVqzOwl4GvAGo7cCOgU4DkzexG4EfhGFHWLdIXuByJSZWb2PHC6u6fbzN8AnObub8dTmUjX6CgskSpz93bdT8GtTnMKDzmaqAUiIiJl0RiIiIiURQEiIiJlUYCIiEhZFCAiIlIWBYiIiJRFASIiImVRgIiISFn+P8t+9/18N7LTAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"SL=2.5e-6\n",
"RD=2e-5\n",
"\n",
"seq=L.Sequence().add_channel('e',t=[0,pi2,pi2+SL,RD],v1=[v1,v1,0],phase=[0,np.pi/2,0])\n",
"\n",
"rho=sl.Rho('Thermal',['1Hz','ez','ey'])\n",
"rho.DetProp(seq,n=100,n_per_seq=100)\n",
"_=rho.plot(axis='us')"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "0e6a9826",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Enhancement: 100\n"
]
}
],
"source": [
"print(f'Enhancement: {rho.I[0].real.max()/ex.Peq[0]:.0f}')"
]
},
{
"cell_type": "markdown",
"id": "38aa7ca4",
"metadata": {},
"source": [
"In this case, the nuclear magnetization stays at its maximum by turning off the spin-lock after the maximum is reached. Little changes on the magnetization otherwise, except a small amount of electron $T_1$ recovery.\n",
"\n",
"While the nucleus is enhanced, we wonder if it is possible to achieve a higher enhancement with repeated transfers. Then, we need to include a delay between repeated sequences. First we try to set the recycle delay to the electron $T_1$."
]
},
{
"cell_type": "markdown",
"id": "19f2199a",
"metadata": {},
"source": [
"### Recycle the sequence"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "51ab0256",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"SL=0.25e-5\n",
"RD=1.4e-3\n",
"\n",
"seq=L.Sequence().add_channel('e',t=[0,pi2,pi2+SL,RD],v1=[v1,v1,0],phase=[0,np.pi/2,0])\n",
"\n",
"rho=sl.Rho('Thermal',['1Hz','ez','ey'])\n",
"rho.DetProp(seq,n=100,n_per_seq=100)\n",
"rho.DetProp(seq,n=100)\n",
"\n",
"ax=plt.subplots(1,2,figsize=[8,4])[1]\n",
"rho.plot(axis='us',ax=ax[0])\n",
"ax[0].set_xlim([-10,1400])\n",
"_=rho.plot(axis='ms',ax=ax[1])"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "688017d4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Enhancement: 161\n"
]
}
],
"source": [
"print(f'Enhancement: {rho.I[0].real.max()/ex.Peq[0]:.0f}')"
]
},
{
"cell_type": "markdown",
"id": "0b6a19a4",
"metadata": {},
"source": [
"We increase the enhancement, but still not to the theoretical max of 657. We notice that the electron z-magnetization equilibrates at a fraction of its original polarization. One option to improve the enhancement is to increase the recycle delay to give the electron more chance to recover. Here, we take $5\\cdot T_1$ to obtain nearly fully recovery."
]
},
{
"cell_type": "markdown",
"id": "2d17c35e",
"metadata": {},
"source": [
"### Use longer relaxation delay ($5\\cdot T_{1e}$)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "25694ba5",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"SL=0.25e-5\n",
"RD=1.4e-3*5\n",
"\n",
"seq=L.Sequence().add_channel('e',t=[0,pi2,pi2+SL,RD],v1=[v1,v1,0],phase=[0,np.pi/2,0])\n",
"\n",
"rho=sl.Rho('Thermal',['1Hz','ez','ey'])\n",
"rho.DetProp(seq,n=100,n_per_seq=100)\n",
"rho.DetProp(seq,n=200)\n",
"\n",
"fig,ax=plt.subplots(1,2,figsize=[8,4])\n",
"rho.plot(axis='us',ax=ax[0])\n",
"ax[0].set_xlim([-10,1400])\n",
"rho.plot(axis='ms',ax=ax[1])\n",
"fig.tight_layout()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "3a63b836",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Enhancement: 256\n"
]
}
],
"source": [
"print(f'Enhancement: {rho.I[0].real.max()/ex.Peq[0]:.0f}')"
]
},
{
"cell_type": "markdown",
"id": "9ec4be3a",
"metadata": {},
"source": [
"### Optimize relaxation delay for fast-relaxing nuclei"
]
},
{
"cell_type": "markdown",
"id": "78ca6e6a",
"metadata": {},
"source": [
"The improvement is far more pronounced. Since the electron recovers full after every step, much more electron polarization is available to transfer to the nucleus. In our example here, the nuclear $T_1$ is about 1000 times longer than that of the electron, so there isn't really any compromise on the recycle delay between the electron recovering and the nucleus losing magnetization. However, in a real system, losses on the nuclei are much more pronounced, because the magnetization spreads among many protons. Let's mimick this by shortening the nuclear T1 by a factor of 500 (if spread of polarization among the nuclei were infinitely fast, the rate of magnetization loss would be enhanced by the number of nuclei). Then, we optimize the recycle delay for this situation. \n",
"\n",
"Since this optimization takes some time, we go to a single crystallite. Note that if the hyperfine coupling is aligned along the *z*-axis or the *xy*-plane, the pseudosecular coupling will vanish, eliminating the NOVEL transfer. Therefore, we use the 'alpha0beta45' powder average, which just has one set of Euler angles ($\\alpha=0^\\circ$, $\\beta=45^\\circ$, $\\gamma=0^\\circ$)\n",
"\n",
"To get the true optimimum, we would need to include the powder average, but for sake of example, this is sufficient."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "34490b3c",
"metadata": {},
"outputs": [],
"source": [
"ex.pwdavg='alpha0beta45'\n",
"L.clear_relax()\n",
"\n",
"L.add_relax(Type='T2',i=0,T2=5e-3,OS=True)\n",
"L.add_relax(Type='T2',i=1,T2=.890e-6,OS=True)\n",
"L.add_relax(Type='T1',i=0,T1=13.7/500,OS=True,Thermal=True)\n",
"L.add_relax(Type='T1',i=1,T1=1.4e-3,OS=True,Thermal=True)\n",
"\n",
"v1=212e6\n",
"pi2=1/v1/4\n",
"SL=0.25e-5\n",
"rho=sl.Rho('Thermal','1Hz')\n",
"\n",
"RD0=np.linspace(0.5,5,50)*1.4e-3\n",
"e=[]\n",
"\n",
"for RD in RD0:\n",
" seq=L.Sequence().add_channel('e',t=[0,pi2,pi2+SL,RD],v1=[v1,v1,0],phase=[0,np.pi/2,0])\n",
" rho.clear()\n",
" #A sequence or propagator raised to infinity finds the equilibrium density matrix\n",
" (seq**np.inf*rho)()\n",
" e.append(rho.I[0][0].real/ex.Peq[0])"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "77a16a9f",
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax=plt.subplots()[1]\n",
"ax.plot(RD0*1e3,e)\n",
"ax.set_xlabel('RD / ms')\n",
"_=ax.set_ylabel('Enhancement')"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "1f3965f3",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Maximum enhancement of 192 at RD=3.8 ms\n"
]
}
],
"source": [
"i=np.argmax(e)\n",
"print(f'Maximum enhancement of {e[i]:.0f} at RD={RD0[i]*1e3:.1f} ms')"
]
},
{
"cell_type": "markdown",
"id": "4f5e3074",
"metadata": {},
"source": [
"### Re-optimize spin-lock length"
]
},
{
"cell_type": "markdown",
"id": "0f307b8d",
"metadata": {},
"source": [
"We return now to the longer nuclear $T_1$. A remaining question is: why can't we actually achieve the full theoretical enhancement of 657, if the nuclear relaxation is so slow? \n",
"\n",
"The problem is that the while for one repetition of the NOVEL sequence, the optimal $^1H$ polarization occured at about 2.5 μs. However, significant electron polarization loss has already occured for a spin-lock of that length, given the $T_2$ of 0.89 μs (note under the spin-lock, the effective $T_{1\\rho}$ becomes twice the set value of $T_2$). So, we can also optimize the spin-lock length (using $5\\cdot T_1$ for the recycle delay)."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "67365442",
"metadata": {},
"outputs": [],
"source": [
"L.clear_relax()\n",
"\n",
"L.add_relax(Type='T2',i=0,T2=5e-3,OS=True)\n",
"L.add_relax(Type='T2',i=1,T2=.890e-6,OS=True)\n",
"L.add_relax(Type='T1',i=0,T1=13.7,OS=True,Thermal=True)\n",
"L.add_relax(Type='T1',i=1,T1=1.4e-3,OS=True,Thermal=True)\n",
"\n",
"v1=212e6\n",
"pi2=1/v1/4\n",
"SL=0.25e-5\n",
"RD=5*1.4e-3\n",
"rho=sl.Rho('Thermal','1Hz')\n",
"\n",
"SL0=np.linspace(0,2.5e-6,200)\n",
"e=[]\n",
"\n",
"for SL in SL0:\n",
" seq=L.Sequence().add_channel('e',t=[0,pi2,pi2+SL,RD],v1=[v1,v1,0],phase=[0,np.pi/2,0])\n",
" rho.clear()\n",
" #A sequence or propagator raised to infinity finds the equilibrium density matrix\n",
" (seq**np.inf*rho)()\n",
" e.append(rho.I[0][0].real/ex.Peq[0])"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "a450fe34",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax=plt.subplots()[1]\n",
"ax.plot(SL0*1e6,e)\n",
"ax.set_xlabel('Spin-lock length / $\\mu$s')\n",
"_=ax.set_ylabel('Enhancement')"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "3f48f671",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Maximum enhancement of 574 at SL=0.23 μs\n"
]
}
],
"source": [
"i=np.argmax(e)\n",
"print(f'Maximum enhancement of {e[i]:.0f} at SL={SL0[i]*1e6:.2f} μs')"
]
},
{
"cell_type": "markdown",
"id": "ddf45ab0",
"metadata": {},
"source": [
"Finally, we are close to the maximum enhancement. We plot the buildup of that polarization below"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "53b09f4e",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"SL=SL0[i]\n",
"seq=L.Sequence().add_channel('e',t=[0,pi2,pi2+SL,RD],v1=[v1,v1,0],phase=[0,np.pi/2,0])\n",
"rho.clear()\n",
"rho.DetProp(seq,n=500)\n",
"ax=rho.plot(axis='s')\n",
"ax.plot([0,rho.t_axis[-1]],-np.ones(2)*ex.Peq[1],color='grey',linestyle=':',label=r'|e$^-$ thermal polar.|')\n",
"_=ax.legend()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "c8b8ee4e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Maximum enhancement of 572, 95% of max reached at 1.79 s\n"
]
}
],
"source": [
"i=np.argmax(rho.I[0]/rho.I[0][-1]>0.95)\n",
"print(f'Maximum enhancement of {rho.I[0][-1].real/ex.Peq[0]:.0f}, 95% of max reached at {rho.t_axis[i]:.2f} s')"
]
},
{
"cell_type": "markdown",
"id": "98e15fc5",
"metadata": {},
"source": [
"### Buildup with varying spin-lock length"
]
},
{
"cell_type": "markdown",
"id": "3658c21c",
"metadata": {},
"source": [
"While the enhancement is optimized, the buildup is quite slow. A shorter spin-lock is required to achieve the maximum enhancement, but this makes a very inefficient buildup at the beginning of the sequence, where we saw at the beginning of this section that the maximum enhancement came much later, at 2.5 μs. Here, we see what happens if we vary the spin-lock length, from long to short (2.5 μs to 0.2 μs), during the buildup."
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "f615d41b",
"metadata": {},
"outputs": [],
"source": [
"rho=sl.Rho('Thermal','1Hz')\n",
"\n",
"SL0=0.2e-6+np.exp(-np.linspace(0,1,100)*20)*(2.5e-6-0.2e-6)\n",
"\n",
"for SL in SL0:\n",
" seq=L.Sequence().add_channel('e',t=[0,pi2,pi2+SL,RD],v1=[v1,v1,0],phase=[0,np.pi/2,0])\n",
" #A sequence or propagator raised to infinity finds the equilibrium density matrix\n",
" seq**5*rho() #Makes a total of 500*RD"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "54974fd3",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax=rho.plot(axis='s')\n",
"ax.plot([0,rho.t_axis[-1]],-np.ones(2)*ex.Peq[1],color='grey',linestyle=':',label=r'|e$^-$ thermal polar.|')\n",
"_=ax.legend()"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "4335e6dd",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Maximum enhancement of 572, 95% of max reached at 0.70 s\n"
]
}
],
"source": [
"i=np.argmax(rho.I[0]/rho.I[0][-1]>0.95)\n",
"print(f'Maximum enhancement of {rho.I[0][-1].real/ex.Peq[0]:.0f}, 95% of max reached at {rho.t_axis[i]:.2f} s')"
]
},
{
"cell_type": "markdown",
"id": "6d61a174",
"metadata": {},
"source": [
"Above, we've set up the calculation such that the spin-lock length starts at 2.5 μs and ends at 0.2 μs, where a decaying exponential defines the transition between the two values (the time constant of this decay has been optimized by hand, the choice of an exponential is only a guess). As we see 95% of the maximum enhancement is reached much more quickly than with a fixed spin-lock length."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 5
}