National scientific research cooperation plays an important role in the development of national scientific research capabilities. Quantitative analysis of scientific cooperation between countries can provide references for guiding the country to select scientific research partners. Based on the 356,405 papers on the AMiner platform from 1953 to 2010, we analyze the collaboration patterns and its evolution of papers between 51 countries. From the perspectives of national scientific cooperation network, considering paper output and academic influence, we compare cooperation network centrality, collaboration intensity, cooperation relationship selection and other indicators to analyze the relationship of scientific cooperation. Several interesting patterns are observed: (1) the scientific cooperation among countries is very frequent, but most of the cooperative relations between them are weak; (2) there are some special super ties between countries; (3) super ties occur at an average rate of 1 in 7 collaborators; (4) the average cooperation strength of high-yielding countries is generally higher than that of low-yielding countries; (5) when high-yielding countries become strong relations with low-yielding countries, it can greatly drive the growth of scientific research output of high-yielding countries. Then, the regression method is used to measure the impact of super ties on the publication rate and citations of countries, controlling pertinent factors such as prestige, cooperation strength, and cooperation scale. The regression results indicate that super ties increase the productivity and citations of national papers, confirming that super-tie is an important driving factor in the development of science.